How to Upgrade iCloud storage
How to Upgrade iCloud storage While I’m using my wife’s phone
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You can only do this on an iOS device, Mac or Windows signed in to your Apple ID - I assume your wife's phone is signed into a different Apple ID? You would have to get her to sign out of iCloud and then sign in with your ID and this is going to be more hassle than it's worth. If you can use a computer it would be easier.
Buy more iCloud storage - Apple Support